With his race still unresolved, Georgia Republican gubernatorial candidate Brian Kemp resigned his position as the state's top election official and declared victory, drawing a strong rebuke from Democrat Stacey Abrams, whose campaign estimated that there were thousands of ballots outstanding or unaccounted for.

Kemp announced at a news conference with Republican Gov. Nathan Deal that he had submitted his resignation as secretary of state and would begin preparing to take over as governor.

"We won the race," Kemp told reporters. "It's very clear now. We are moving forward with the transition."

Kemp had 50.3 percent of the vote to Abrams's 48.7 percent as of midday Thursday, according to the Associated Press. But the Abrams campaign argued that balloting had been grossly mishandled, citing reports of voting hurdles and problems with vote-counting.

A similar debate is emerging in Florida, where Democratic gubernatorial candidate Andrew Gillum appeared to back off his election-night concession to Republican Ron DeSantis, citing reports of uncounted ballots.

"Our campaign . . . is monitoring the situation closely and is ready for any outcome, including a state-mandated recount," the campaign said Thursday in a statement.

Reports of voting problems were prevalent in both Georgia and Florida, where Abrams and Gillum ran to be their states' first black governors.

Democratic National Committee Chairman Tom Perez said that Democrats had "boots on the ground" in Georgia and were monitoring the possibility of recounts in Florida.

In both states, they were coordinating with campaigns to see whether provisional ballots, or absentee ballots rejected because signatures didn't match - an election standard that Democrats consider to be voter suppression - were being counted.

"We've got folks on our voter protection team right now, chasing provisional ballots," Perez said at a breakfast roundtable sponsored by the Christian Science Monitor. "They claim there are something like 22,000 or 25,000 provisional ballots still out in Georgia. I'll be honest with you; I don't believe them. I think there's more. The problem is that the fox is guarding the henhouse; the person who wants to be governor is overseeing the integrity of the election."

Perez also suggested that the close statewide races in Florida could change if every vote cast was counted, a process that could well involve lawsuits.

"There's an army of lawyers down there now that are working on the recount, and I'm glad they're doing that," said Perez. "Voter suppression is a permanent staple in the [Republican] playbook and that's a lesson that we have to learn as a party."

In Georgia, Kemp's margin had narrowed Wednesday as election officials counted outstanding ballots. If his share of the vote falls below 50 percent, he and Abrams would face each other in a runoff election.

At a news conference, lawyers for the Abrams campaign announced that they were filing a preliminary lawsuit in Dougherty County over problems with mail-in ballots and weighing other possible litigation.

"We are not stopping until we are confident that every vote has been counted," said Abrams campaign manager Lauren Groh-Wargo.

Georgia voters described hours-long lines Tuesday and polling places that struggled with a shortage of voting machines, broken equipment and a dearth of printed provisional ballots.

Noting that many of the reports came from communities with large minority populations, voting rights advocates charged Kemp with using his power as the state's chief election official to interfere with the race. Kemp has strongly denied claims of impropriety.

"The integrity of the process has been clear in Georgia," he said Thursday. "The election integrity is beyond doubt."

Nonprofit group Protect Democracy said Kemp's resignation came just before a federal court hearing in its lawsuit seeking to stop him from overseeing the governor's race.

"This is a huge victory for democracy and the rule of law," Larry Schwartztol, counsel for Protect Democracy, said in a statement. "It is a basic constitutional principle that a person may not be a judge in their own case and that's what Brian Kemp was attempting to be here."

Kemp called the lawsuit, as well as others filed in the race, "quite honestly, ridiculous."

"We're going to continue to fight that," he said. "The votes are not there for her."

Wrangling over gubernatorial balloting in Florida and Georgia came as several key races remained unresolved around the country, including Senate races in Arizona and Florida and close to a dozen House races.

In the Florida Senate race, Republican Rick Scott had 50.1 percent of the vote as of Thursday afternoon, while Democratic incumbent Bill Nelson had 49.9 percent, according to the AP.

Marc Elias, a prominent election lawyer representing Nelson's campaign, predicted a recount and an eventual Nelson victory. He said the margin between the two campaigns was now less than 22,000 votes.

"I think it's fair to say right now the results of the 2018 Senate election are unknown, and [the media] and elections officials should treat it as such," Elias said on a conference call with reporters.

Elias said he was not sure whether Nelson would be in the lead going into a recount.

"I would say, you know, it's a jump ball," he said. "We may be up by 5,000 votes, we may be down by 5,000 votes. I think either way, we're going to be in a recount."

Scott's campaign - as well as Florida Republican Sen. Marco Rubio - painted Elias as a hired gun from Washington, D.C., whose intention was to "steal" the election.

"It is sad and embarrassing that Bill Nelson would resort to these low tactics after the voters have clearly spoken. Maybe next, he'll start ranting that Russians stole the election from him," Scott's campaign said in a statement.

Elias is known for his ties to leading Democrats and served as general counsel for Hillary Clinton's 2016 presidential campaign.

Handel, who won her seat last year in a special election, wrote on Facebook that she "came up a bit short" in Tuesday's midterms.

"Congratulations to Representative-Elect Lucy McBath and I send her only good thoughts and much prayer for the journey that lies ahead for her," Handel wrote Thursday.

McBath will come to Congress as part of the House's new Democratic majority. Her victory marked the party's 29th pickup in the lower chamber, with several races still undecided, according to a tally by The Washington Post.

McBath was a first-time congressional candidate who jumped into the race at the last minute, citing February's mass shooting at Marjory Stoneman Douglas High School in Parkland, Florida, that left 17 dead. She became an activist after her 17-year-old son was fatally shot in 2012 by a man who had argued with the teen and his friends about loud music coming from their car.

Several political forecasters had moved the race in Georgia's 6th Congressional District from "leans Republicans" to "toss-up" over the weekend. The Associated Press reported that McBath got 50.5 percent of the vote to Handel's 49.5 percent, with 100 percent of precincts reporting.

Handel's short-lived tenure in the House came after she beat Democrat Jon Ossoff in the 2017 special election to replace outgoing Rep. Tom Price (R-Ga.), who left to become President Trump's first secretary of health and human services.

The race drew national attention as an early referendum on Trump in a district Republicans had held since 1979.

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The Washington Post's Amy Gardner, Sean Sullivan and David Weigel contributed to this report.